Continuous-Time Mean Field Games with Finite State Space and Common Noise

Abstract

We formulate and analyze a mathematical framework for continuous-time mean field games with finitely many states and common noise. The key insight is that we can circumvent the master equation and reduce the mean field equilibrium to a system of forward-backward systems of (random) ordinary differential equations by conditioning on common noise events. In the absence of common noise, our setup reduces to that of Gomes, Mohr and Souza (2013) and Cecchin and Fischer (2020).

Keywords: mean field games, common noise, Markov chains, regime shifts

JEL Classification: C61, C73